The ground state energy of the two dimensional Ginzburg–Landau functional with variable magnetic field
K. Attar
Laboratoire de Mathématiques, Université Paris-Sud, Rue G. Clémenceau, Bât 425, F-91405 Orsay Cedex, France, Laboratoire de Mathématiques, Université Libanaise, Hadath, Beyrouth, Liban
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Abstract
We consider the Ginzburg–Landau functional with a variable applied magnetic field in a bounded and smooth two dimensional domain. We determine an accurate asymptotic formula for the minimizing energy when the Ginzburg–Landau parameter and the magnetic field are large and of the same order. As a consequence, it is shown how bulk superconductivity decreases in average as the applied magnetic field increases.
Cite this article
K. Attar, The ground state energy of the two dimensional Ginzburg–Landau functional with variable magnetic field. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), no. 2, pp. 325–345
DOI 10.1016/J.ANIHPC.2013.12.002